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Izv. Vyssh. Uchebn. Zaved. Mat., 2017, Number 8, Pages 53–61 (Mi ivm9268)  

This article is cited in 1 scientific paper (total in 1 paper)

Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient

R. M. Safina

Volga Region State Academy of Physical Culture, Sport and Tourism, 35 Universiade Village, Kazan, 420138 Russia

Abstract: For a mixed-type equation of the second kind with a singular coefficient with the use of spectral expansions, we establish a uniqueness criterion for solving the problem with incomplete boundary data. The solution is constructed in the form of the Fourier–Bessel sums. In substantiation of the uniform convergence we establish an estmate on separation from zero of small denominator with the corresponding asymptotic behavior that allowed to substantiate the convergence of the series in the class of regular solutions.

Keywords: mixed type equation, Keldysh problem, singular coefficient, spectral method, uniqueness, Fourier–Bessel series, small denominators.

Funding Agency Grant Number
Russian Foundation for Basic Research 16-31-50008_мол_нр


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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2017, 61:8, 46–54

Bibliographic databases:

UDC: 517.957
Received: 14.04.2016

Citation: R. M. Safina, “Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 8, 53–61; Russian Math. (Iz. VUZ), 61:8 (2017), 46–54

Citation in format AMSBIB
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\by R.~M.~Safina
\paper Keldysh problem for mixed type equation with strong characteristic degeneration and singular coefficient
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2017
\issue 8
\pages 53--61
\mathnet{http://mi.mathnet.ru/ivm9268}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2017
\vol 61
\issue 8
\pages 46--54
\crossref{https://doi.org/10.3103/S1066369X17080059}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85024913201}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. K. T. Karimov, “Zadacha Keldysha dlya trekhmernogo uravneniya smeshannogo tipa s tremya singulyarnymi koeffitsientami v polubeskonechnom parallelepipede”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 30:1 (2020), 31–48  mathnet  crossref
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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